Question

What is the true weight of an object in a geostationary satellite that weighed exactly 10.0 N at the north pole?

Answer 1

Answer:

it Weight 15kg if the sattilte is strong

Answer 2

The object in the geostationary satellite has the true weight 0.23 N.

Explanation:

The object’s weight is inversely proportional to the distance’s square from the centre.

At north pole, the weight is   $W_{p} \propto \frac{1}{R^{2}}$

At equator, the satellite’s weight,   $\mathrm{W}_{\mathrm{e}} \propto \frac{1}{(\mathrm{R}+\mathrm{h})^{2}}$

where h is the distance.

Now,   $\frac{\mathrm{W}_{\mathrm{p}}}{\mathrm{W}_{\mathrm{e}}}=\frac{(\mathrm{R}+\mathrm{h})}{\mathrm{R}^{2}}$

$\Rightarrow \mathrm{W}_{\mathrm{e}}=\frac{\mathrm{W}_{\mathrm{p}} \mathrm{R}^{2}}{(\mathrm{R}+\mathrm{h})^{2}}$

It is given that $\mathrm{W}_{\mathrm{p}}=10 \mathrm{N}$ .  

The geostationary satellite has the height,   $\mathrm{h}=36000 \mathrm{km}$

We = $10 \times \frac{64002}{(6400+36000)^{2}}=0.227 N$

The weight is approximately 0.23 N.